When these animations are made by experts, they are actually not abstractions. Animations like this one [https://www.youtube.com/watch?v=X_tYrnv_o6A] actually don't show you an "idea" of how this looks but the actual shape of the individual molecules involved.
The reason we can now for many proteins draw pictures of how the molecule looks on the tiny scale that it is, is the field of structural biology. The scientists working in this field use techniques like X-ray crystallography, nuclear magnetic reconance spectroscopy and cryogenic electron microscopy to determine the structure of a protein at resolutions down to 2.7 Å (Angstrom, 1Å = 0.1nm). Once they manage to get a reliable picture of how a protein molecule looks, they publish their work and submit it to the world-wide protein data bank, which you can access freely using one of three websites: PDBe, PDBj and RCSB.
I tried searching for the proteins in your animation (CD4 and the HIV envelope protein gp120). Some structures do exist for them (e.g. http://www.ebi.ac.uk/pdbe/entry/pdb/2ny1) but they seem to contain only part of what's shown in the animation. Often certain parts of proteins can't be identified by structural biology for technical reasons, but we know they must be there based on the genetic information we have, and we can make some educated guesses about what those bits of the protein might look like. It seems in this animation, there was quite a bit of educated guessing involved.
A lot of biological science nowadays goes by the paradigm "seeing is believing". Many modern animations are reproduced from actual recordings where the process shown in the animation can be seen happening in reality. Cell divison for example is an intensively researched process that has been filmed using many different microscopic techniques and focussing on many different parts of the cell, figuring out what each protein or other molecule does during the process. Putting together knowledge from many different teams, you can generate a full picture of what everything is doing at the same time.
As far as reading recommendations go, any basic molecular biology textbook like Molecular Biology of the Cell by Alberts et al. (pick it up from a library), or lectures freely available online should allow you to gradually wrap your head around it.